docs(markdown): update mathjax3 install instructions in markdown guides

[rockyxwall]

Description

When you copy the old command markdown-it-mathjax3^4, it fails because the syntax is invalid.
This PR replaces that example with correct code-group install commands for all package managers and adds a note recommending markdown-it-mathjax3@^4 due to breaking changes in newer versions.
All language versions of the markdown guide have been updated.

Linked Issues

Not applicable, documentation correction.

[brc-dd]

For which package manager is it broken?

[rockyxwall]

For which package manager is it broken?

It is a syntax error. The package works fine, but as I was new and did not know that you have to write mathjax3^4 as mathjax3@^4

When you run npm add -D markdown-it-mathjax3^4, you get this error:
npm error code EINVALIDTAGNAME npm error Invalid tag name "markdown-it-mathjax3^4" of package "markdown-it-mathjax3^4": Tags may not have any characters that encodeURIComponent encodes. npm error A complete log of this run can be found in: C:\Users\admin\AppData\Local\npm-cache\_logs\2025-12-06T15_33_23_420Z-debug-0.log

and for pnpm add -D markdown-it-mathjax3^4, you get this error:
ERR_PNPM_FETCH_404  GET https://registry.npmjs.org/markdown-it-mathjax34: Not Found - 404 This error happened while installing a direct dependency of B:\1Files\username\02_Codeing\01_Github\Lazy-Study-Doc markdown-it-mathjax34 is not in the npm registry, or you have no permission to fetch it. No authorization header was set for the request.

So what I did was just remove the ^4 and install the latest mathjax3 that is v5 now. But with v5 of mathjax3, VitePress does not work at all, as shown in the guide, you have to install v4. Just by adding a @ before ^4 fixes the issue if it's an issue at all. It's just a syntax error.

[brc-dd]

Ah, I see it was a typo earlier. @ should’ve been there. I still don’t think a note or code block is needed. The commands could simply be fixed. Also, we will be removing that plugin soon.

[rockyxwall]

Ah, I see it was a typo earlier. @ should’ve been there. I still don’t think a note or code block is needed. The commands could simply be fixed. Also, we will be removing that plugin soon.

Oh yes, you are right, I also had put English in all other languages... I just fixed the commands and removed everything else.